Petroleum exploration operations include the analysis of logging parameters to determine a formation representation. In an exemplary operation, a formation representation can be obtained by correlating the logging parameter to a low-resolution seismic volume parameter such as an seismic interval velocity obtained at equivalent depths. In such an operation, the correlation includes a least-square regression of the logging parameter. A typical assumption of the least-squares regression is that measurement errors occur only in the logging parameter measurements and not in the seismic interval velocity measurements. Also, it is assumed that non-systematic errors are normally distributed. These assumptions are typically incorrect, so that the least-squares regression generally does not provide a full representation of formation characteristics. The present disclosure therefore provides a method for determining a correlation for logging parameters and a seismic volume parameter that provides a better representation of the formations and associated uncertainties in the three-dimensional volume.